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|0 1J (a) Write A in terms of A and I. (b) Find A5 for the matrix Similarly, multiplying both sides of the equation A² = 2A + I by A gives A³ in terms of A², A, and I. Moreover, you can write A³ in terms of A and I by replacing A² with 2A + I, as shown below. A³ = 2A² + A = 2 (2A + I) + A = 5A+2I 4-1 го о A = 2 2 -1 1 0 2 (Hint: Find the characteristic polynomial of A, then use the Cayley-Hamilton Theorem to write A³ in terms of A², A, and I. Inductively write A5 in terms of A², A, and I.)

|0 1J (a) Write A in terms of A and I. (b) Find A5 for the matrix Similarly, multiplying both sides of the equation A² = 2A + I by A gives A³ in terms of A², A, and I. Moreover, you can write A³ in terms of A and I by replacing A² with 2A + I, as shown below. A³ = 2A² + A = 2 (2A + I) + A = 5A+2I 4-1 го о A = 2 2 -1 1 0 2 (Hint: Find the characteristic polynomial of A, then use the Cayley-Hamilton Theorem to write A³ in terms of A², A, and I. Inductively write A5 in terms of A², A, and I.)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Help me with gayley-Hamilton Theorem
or So, A2 is written in terms of A and I. (a) Write A4 in terms of A and I. (b) Find A5 for the matrix F5 % A² = 2A+I=2 ² Q Search Similarly, multiplying both sides of the equation A² = 2A + I by A gives A³ in terms of A², A, and I. Moreover, you can write A³ in terms of A and I by replacing A2 with 2A + I, as shown below. A³ = 2A² + A = 2 (2A+I) + A = 5A+2I 30+ F6 A² = 2A + I. F7 [3 -1 & A = (Hint: Find the characteristic polynomial of A, then use the Cayley-Hamilton Theorem to write A³ in terms of A², A, and I. Inductively write A5 in terms of A², A, and I.) 0 F8 00 1 22-1 10 2 ☀ 2 F9 F10 147 F11 F12
Transcribed Image Text:or So, A2 is written in terms of A and I. (a) Write A4 in terms of A and I. (b) Find A5 for the matrix F5 % A² = 2A+I=2 ² Q Search Similarly, multiplying both sides of the equation A² = 2A + I by A gives A³ in terms of A², A, and I. Moreover, you can write A³ in terms of A and I by replacing A2 with 2A + I, as shown below. A³ = 2A² + A = 2 (2A+I) + A = 5A+2I 30+ F6 A² = 2A + I. F7 [3 -1 & A = (Hint: Find the characteristic polynomial of A, then use the Cayley-Hamilton Theorem to write A³ in terms of A², A, and I. Inductively write A5 in terms of A², A, and I.) 0 F8 00 1 22-1 10 2 ☀ 2 F9 F10 147 F11 F12
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